The component of vector $\vec{A}=2 \hat{i}+3 \hat{j}$ along the direction of $(\hat{i}-\hat{j})$ is

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(b) : Given : $\vec{A}=2 \hat{i}+3 \hat{j}, \vec{B}=\hat{i}-\hat{j}$ (say) Component of $\vec{A}$ along the direction of $\vec{B}$ \ $ =\frac{\vec{A} \cdot \vec{B}}{|B|}=\frac{(2 \hat{i}+3 \hat{j}) \cdot(\hat{i}-\hat{j})}{\sqrt{2}}=-\frac{1}{\sqrt{2}} $